You are complaining about something that is not specific to Apple Music. It can happen, and it sucks, but Apple is no different from any other online music purchasing store in this regard.
iTunes Store purchases are free from DRM and can be backed up just like any other libre digital purchases.
All songs offered by the iTunes Store come without Digital Rights Management (DRM) protection. These DRM-free songs, called iTunes Plus, have no usage restrictions and feature high-quality, 256 kbps AAC (Advanced Audio Coding) encoding.
https://support.apple.com/guide/music/intro-to-the-itunes-store-mus3e2346c2/mac